We present a method for specifying temporal constraints on trajectories of dynamical systems and enforcing them during qualitative simulation. This capability can be used to focus a simulation, simulate non-autonomous and piecewise-continuous systems, reason about boundary condition problems and incorporate observations into the simulation. The method has been implemented in TeQSIM, a qualitative simulator that combines the expressive power of qualitative differential equations with temporal logic. It interleaves temporal logic model checking with the simulation to constrain and refine the resulting predicted behaviors and to inject discontinuous changes into the simulation.

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